# Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties

Izak Broere; Jozef Bucko; Peter Mihók

Discussiones Mathematicae Graph Theory (2002)

- Volume: 22, Issue: 1, page 31-37
- ISSN: 2083-5892

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topIzak Broere, Jozef Bucko, and Peter Mihók. "Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties." Discussiones Mathematicae Graph Theory 22.1 (2002): 31-37. <http://eudml.org/doc/270442>.

@article{IzakBroere2002,

abstract = {Let ₁,₂,...,ₙ be graph properties, a graph G is said to be uniquely (₁,₂, ...,ₙ)-partitionable if there is exactly one (unordered) partition V₁,V₂,...,Vₙ of V(G) such that $G[V_i] ∈ _i$ for i = 1,2,...,n. We prove that for additive and induced-hereditary properties uniquely (₁,₂,...,ₙ)-partitionable graphs exist if and only if $_i$ and $_j$ are either coprime or equal irreducible properties of graphs for every i ≠ j, i,j ∈ 1,2,...,n.},

author = {Izak Broere, Jozef Bucko, Peter Mihók},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {induced-hereditary properties; reducibility; divisibility; uniquely partitionable graphs.; partitionable graphs; graph properties; partition; irreducible properties},

language = {eng},

number = {1},

pages = {31-37},

title = {Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties},

url = {http://eudml.org/doc/270442},

volume = {22},

year = {2002},

}

TY - JOUR

AU - Izak Broere

AU - Jozef Bucko

AU - Peter Mihók

TI - Criteria for of the existence of uniquely partitionable graphs with respect to additive induced-hereditary properties

JO - Discussiones Mathematicae Graph Theory

PY - 2002

VL - 22

IS - 1

SP - 31

EP - 37

AB - Let ₁,₂,...,ₙ be graph properties, a graph G is said to be uniquely (₁,₂, ...,ₙ)-partitionable if there is exactly one (unordered) partition V₁,V₂,...,Vₙ of V(G) such that $G[V_i] ∈ _i$ for i = 1,2,...,n. We prove that for additive and induced-hereditary properties uniquely (₁,₂,...,ₙ)-partitionable graphs exist if and only if $_i$ and $_j$ are either coprime or equal irreducible properties of graphs for every i ≠ j, i,j ∈ 1,2,...,n.

LA - eng

KW - induced-hereditary properties; reducibility; divisibility; uniquely partitionable graphs.; partitionable graphs; graph properties; partition; irreducible properties

UR - http://eudml.org/doc/270442

ER -

## References

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- [6] P. Mihók, Additive hereditary properties and uniquely partitionable graphs, in: M. Borowiecki and Z. Skupień, eds., Graphs, hypergraphs and matroids (Zielona Góra, 1985) 49-58. Zbl0623.05043
- [7] P. Mihók, Unique factorization theorem, Discuss. Math. Graph Theory 20 (2000) 143-154, doi: 10.7151/dmgt.1114. Zbl0968.05032

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